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Spatial Multiobjective Optimization of Agricultural Conservation Practices using a SWAT Model and an Evolutionary Algorithm
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A modified nonmonotone BFGS algorithm for unconstrained optimization.

Xiangrong Li1, Bopeng Wang1, Wujie Hu1

  • 1Guangxi Colleges and Universities Key Laboratory of Mathematics and Its Applications, College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi P.R. China.

Journal of Inequalities and Applications
|August 29, 2017
PubMed
Summary
This summary is machine-generated.

A new modified BFGS algorithm enhances unconstrained optimization using a nonmonotone line search. This method offers global and superlinear convergence, outperforming the standard BFGS approach in numerical tests.

Keywords:
BFGS updateglobal convergencenonmonotonesuperlinear convergence

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Area of Science:

  • Numerical Analysis
  • Optimization Theory

Background:

  • Unconstrained optimization is a fundamental problem in applied mathematics and computer science.
  • The Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm is a widely used quasi-Newton method for solving such problems.
  • Enhancing the efficiency and convergence properties of optimization algorithms remains an active research area.

Purpose of the Study:

  • To propose a modified BFGS algorithm for unconstrained optimization problems.
  • To improve the effectiveness and convergence rates of the standard BFGS method.
  • To demonstrate the superiority of the proposed algorithm through numerical experiments.

Main Methods:

  • A modified BFGS algorithm is developed incorporating a nonmonotone line search technique for step size determination.
  • The theoretical convergence properties of the modified algorithm are analyzed, focusing on global and superlinear convergence for generally convex functions.
  • Numerical comparisons are conducted against the standard BFGS method using various test problems.

Main Results:

  • The modified BFGS algorithm successfully utilizes a nonmonotone line search to enhance effectiveness.
  • The algorithm is proven to possess both global and superlinear convergence properties for generally convex functions.
  • Numerical results indicate that the proposed algorithm achieves better performance compared to the standard BFGS method.

Conclusions:

  • The modified BFGS algorithm with a nonmonotone line search is an effective approach for unconstrained optimization.
  • The algorithm offers improved convergence guarantees and practical performance over the traditional BFGS method.
  • This work contributes a valuable enhancement to quasi-Newton optimization techniques.